Modelling uncertainty in financial tail risk: a forecast combination and weighted quantile approach

Abstract: A novel forecast combination and weighted quantile based tail-risk forecasting framework is proposed, aiming to reduce the impact of modelling uncertainty in tail-risk forecasting. The proposed approach is based on a two-step estimation procedure. The first step involves the combination of Value-at-Risk (VaR) forecasts at a grid of quantile levels. A range of parametric and semi-parametric models is selected as the model universe in the forecast combination procedure. The quantile forecast combination weights are estimated by optimizing the quantile loss. In the second step, the Expected Shortfall (ES) is computed as a weighted average of combined quantiles. The quantiles weighting structure for ES forecasting is determined by minimizing a strictly consistent joint VaR and ES loss function of the Fissler-Ziegel class. The proposed framework is applied to six stock market indices and its forecasting performance is compared to each individual model in the universe, a simple average approach and a weighted quantile approach. The forecasting results support the proposed framework.